# On Philomatics and Psychomatics for Combining Philosophy and Psychology with Mathematics

arXiv: https://arxiv.org/abs/2308.13738 · HTML: https://mlsanity.com/paper/2308.13738/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 73 references that are in the map.
- First posted on arXiv 26 Aug 2023.

## Builds on (most cited first, 10 of 10)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Factor Analysis, Probabilistic Principal Component Analysis, Variational Inference, and Variational Autoencoder: Tutorial and Survey](https://mlsanity.com/paper/2101.00734/) (2021)
- [KKT Conditions, First-Order and Second-Order Optimization, and Distributed Optimization: Tutorial and Survey](https://mlsanity.com/paper/2110.01858/) (2021)
- [Generative Adversarial Networks and Adversarial Autoencoders: Tutorial and Survey](https://mlsanity.com/paper/2111.13282/) (2021)
- [Affective Manifolds: Modeling Machine's Mind to Like, Dislike, Enjoy, Suffer, Worry, Fear, and Feel Like A Human](https://mlsanity.com/paper/2208.13386/) (2022)

## Built on by (most cited first, 2 of 2)

- [Wittgenstein's Family Resemblance Clustering Algorithm](https://mlsanity.com/paper/2601.01127/) (2026)
- [Data Evolution by Wittgenstein's Rule Following](https://mlsanity.com/paper/2606.22674/) (2026)

## Abstract (arXiv)

We propose the concepts of philomatics and psychomatics as hybrid combinations of philosophy and psychology with mathematics. We explain four motivations for this combination which are fulfilling the desire of analytical philosophy, proposing science of philosophy, justifying mathematical algorithms by philosophy, and abstraction in both philosophy and mathematics. We enumerate various examples for philomatics and psychomatics, some of which are explained in more depth. The first example is the analysis of relation between the context principle, semantic holism, and the usage theory of meaning with the attention mechanism in mathematics. The other example is on the relations of Plato's theory of forms in philosophy with the holographic principle in string theory, object-oriented programming, and machine learning. Finally, the relation between Wittgenstein's family resemblance and clustering in mathematics is explained. This paper opens the door of research for combining philosophy and psychology with mathematics.